1. What is a quantum material?

2. What do other people say?
Nature Physics, Feb. 2016
Electronic correlations
Topological order
Emergence
Obviously every material is a quantum material, but this term has a specific meaning in the research community, so what do other people say is the definition?
Editorial in nature physics:
Two pillars: systems with electronic correlations and systems with topological order.
Correlations: can’t ignore pairwise coulomb interactions between electrons
Topological order: geometric properties of electronic wavefunction
Together they share a theme of ‘emergence’where the aggregate properties of a many body system cannot be predicted from a reductionist understanding of all the constituents
According to this article, this connection dates back to the 1980s, where two of the most important Nobel prize winning discoveries—high temperature superconductivity and the quantum hall effect---exemplified these two paradigms. However, the connection between these two fields under the umbrella of quantum materials is a relatively new development, as I will discuss in a minute.
Another article makes the contemporary origins of the term more explicit, by pointing out that once upon a time the same research community only focused on correlated systems. This article also points to another unifying theme, materials whose electronic properties cannot be understood from the concepts presented in a solid state textbook written a few decades prior
Physics Today, Sept. 2012
“Quantum materials is a label that has come to signify the area of condensed-matter physics formerly known as strongly correlated electronic systems. Although the field is broad, a unifying theme is the discovery and investigation of materials whose electronic properties cannot be understood with concepts from contemporary condensed-matter textbooks.”

3. History of quantum materials according to Google Scholar
Quantify the emergence of quantum materials a little bit
Procedure:
-Google scholar search, restricted one year at a time
-Picks up phrase in paper, but also authors’ affiliation
-doesn’t normalize for (likely) overall increase in total number of papers every year
Quantum material
-Used in some contexts prior to mid 2000s, but only several 10s of hits per year
-Starts to take off in the mid to late 2000s
-Ideas behind quantum materials have a strong precedent dating back a few decades, but the term itself is really a product of the last decade
Look at the two pillars of the quantum materials field
-Same procedure, google scholar
-Correlated electrons: fairly constant over this period
-Topological insulators etc (which doesn’t capture several related terms): takes off after 2008
Conclusion: The rise of topological order as an emergent phenomenon in materials (not devices) among the research community previously studying emergent phenomena in correlated systems is responsible for the umbrella term ‘quantum materials’
-prior to mid-2000s, this phrase

4. Quantum materials covered in this course
Charge density wave systems (Weeks 3-4)
Superconductors with a focus on unconventional superconductors with electronic correlations (cuprate, iron-based, heavy fermion) (Weeks 5-8)
Topological insulators, other materials with topological surface states, and Dirac materials (Weeks 8-10)
In this course we want to present a small subset of quantum materials, to give you a flavor of some contemporary research directions. This is a course focused on experimental techniques used in the field, specifically a few spectroscopy techniques, which Eduardo will elaborate on in a few minutes.
The materials discussed in this course will be broken up into 3 categories. This makes it sound like we are not covering very much at all, but there is quite bit of depth in each of these topics
Next week: introductions to STM and ARPES
After that: charge density waves
Then: Superconductivity including a general overview and then a more detailed look at materials of contemporary interest
Last: topological insulators and other dirac materials

5. Charge Density Wave (CDW) systems
Symmetry breaking state characterized by standing wave pattern of electrons
Electron-electron and electron-phonon interactions
Purpose in this course
Explain capabilities of all spectroscopies discussed in this course
Many quantum materials, especially lower dimensionality ones, are susceptible to CDW order
Historical/intellectual connection to other topics in this course (e.g. superconductivity)
Begin this course with CDWs because it is perhaps the least abstract concept in this course. As the name implies, a CDW is a standing wave pattern of electrons, and often the crystal lattice will follow the electrons. Both electron-electron and electron-phonon interactions are implicated in this state of matter, and the role of these interactions in producing emergent states of quantum matter is an ongoing theme in this course.
2 weeks of CDW has a very specific purpose in this course:
-it is amenable to all the spectroscopies discussed in this course, so it is a good way to get a feeling for the capabilities of different spectroscopies
-many quantum materials are susceptible to CDW order
-Historical and intellectual connections: example—deep connection between CDW and SC—both have complex order parameter with amplitude and phase, and one of the early theories for superconductivity in metals which had almost all the right ingredients was actually a sliding charge density wave; if you read the literature in condensed matter and materials physics, CDW systems emerge as a trendy topic every decade or so, as this is a common instability in quantum materials, especially in 2 and 3 dimensions
Atomic scale image in charge density wave state of NbSe2.
Source:

6. Unconventional superconductors
Mechanism of superconductivity not explained by Bardeen-Cooper-Schrieffer (BCS) theory which explains superconductivity in simple metals
Strong electron correlations
Sometimes high superconducting transition temperature (Tc)
Normal state above Tc often interesting/anomalous
Next, we move onto the field of superconductors, with a focus on materials whose mechanism we do not understand yet
Definition of unconventional superconductor: not explained by BCS theory
Often have strong correlations, which is one major reason there is no agreed upon theoretical explanation, and a reason they are in the quantum materials camp
Often, but not always, have high Tc—technological interest
Very important: normal state above Tc is often not so normal. Conventional superconductors are simple metals above Tc, unconventional superconductors pretty much always have something more exotic happening. This is one reason we are spending so much of the course on unconventional superconductors: they encompass more than just superconductivity, and their mysterious normal states also exemplify emergent phases of matter relevant to the broader subfield of correlated electrons
SC state characterized by energy gap, which is also related to order parameter of SC state. This energy gap is the way that most spectroscopies couple to superconductivity; it sounds like it is just one number, but this one concept can be quite rich in unconventional superconductors
Image source:

7. Topological insulators and Dirac materials
Topology, instead of symmetry, as the organizing principle of a material’s emergent properties
Insulating interior, robust surface state with a ‘light-like’ (Dirac) dispersion
Dirac materials
Material with Dirac-like dispersion in 1,2,or 3 dimensions
Sometimes have topological and/or exotic surface state
Examples: graphene, topological insulators, topological crystalline insulators, Dirac semimetal, Weyl semimetal
The last topic in this course is the reason that the course title is ‘quantum materials’ not ‘correlated electron systems’. This section of the course will focus on topological insulators and other Dirac materials with topological surface states, and we may also touch on non-topological Dirac materials such as graphene
Topological insulators—topology, not symmetry, as organizing principle. Previous two topics, superconductivity and CDWs are both symmetry breaking states, which onset at a certain temperature; the interesting states in topological insulators are there all the time, as long as time reversal symmetry is maintained (other related materials require other symmetries). A topological insulator is characterized by an insulating interior as illustrated in the top image and metallic surface states, which are not like ordinary surface states because they are very difficult to destroy—they are robust against non-manetic impurities.
Intellectually—precedent is quantum hall effect discovered in 1980s, which also has topological edge state, but requires magnetic field; Tis use strong SO coupling of the materials themselves instead of magnetic field. Practically, materials which are now known to be topological insulators or related materials were previously studied in more applied concepts—such as thermoelectric materials and small gap semiconductors for night vision cameras. This illustrates how investment in materials science and materials physics can pay dividends decades after the fact when these materials are found to have new and unanticipated properties.
In this section of the course, we will cover other dirac materials as time permits. Tis are Dirac materials, as are other materials which have light-like (linear) dispersion in 1,2 or 3D. Many of these have exotic or topological surface states. Examples.
Image sources:

8. Why? Basic science Applications Emergent many-body phases
Connections to other fields of physics
Applications
Electronics
Energy